Spiral instability can drive thermonuclear explosions in binary white dwarf mergers

This is the final version of the article. Available from American Astronomical Society via the DOI in this record.Thermonuclear, or Type Ia supernovae (SNe Ia), originate from the explosion of carbon–oxygen white dwarfs, and serve as standardizable cosmological candles. However, despite their importance, the nature of the progenitor systems that give rise to SNe Ia has not been hitherto elucidated. Observational evidence favors the double-degenerate channel in which merging white dwarf binaries lead to SNe Ia. Furthermore, significant discrepancies exist between observations and theory, and to date, there has been no self-consistent merger model that yields a SNe Ia. Here we show that a spiral mode instability in the accretion disk formed during a binary white dwarf merger leads to a detonation on a dynamical timescale. This mechanism sheds light on how white dwarf mergers may frequently yield SNe Ia.We thank James Guillochon, Lars Bildsten, Matthew Wise, and Gunnar Martin Lellep for useful discussions and Matthias Aegenheyster for his contributions to the FLASH analysis codes. E.G.B. acknowledges support from MCINN grant AYA2011–23102, and from the European Union FEDER fund. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. Simulations at UMass Dartmouth were performed on a computer cluster supported by NSF grant CNS-0959382 and AFOSR DURIP grant FA9550-10-1-0354. This research has made use of NASA's Astrophysics Data System and the yt astrophysics analysis software suite Turk et al. (2011). R.T.F. is grateful to have had the opportunity to complete this paper during a visit to the Kavli Institute for Theoretical Physics, which is supported in part by the National Science Foundation under grant No. NSF PHY11-25915

Topological magnons in CrI3 monolayers: an itinerant fermion description

Magnons dominate the magnetic response of ferromagnetic two-dimensional crystals such as CrI3. Because of the arrangement of Cr spins in a honeycomb lattice, magnons in CrI3 bear a strong resemblance with electrons in graphene. Neutron scattering experiments carried out in bulk CrI3 show the existence of a gap at the Dirac points, conjectured to have a topological nature. We propose a theory for magnons in CrI3 monolayers based on an itinerant fermion picture, with a Hamiltonian derived from first principles. We obtain the magnon dispersion for 2D CrI3 with a gap at the Dirac points with the same Berry curvature in both valleys. For CrI3 ribbons, we find chiral in-gap edge states. Analysis of the magnon wave functions in momentum space confirms their topological nature. Importantly, our approach does not require a spin Hamiltonian, and can be applied to insulating and conducting 2D materials with any type of magnetic order.GVA - Generalitat Valenciana(Prometeo2017/139); European Commission through the project 'Graphene- Driven Revolutions in ICT and Beyond' (reference No. 881603 – Core 3), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2013, COMPETE2020, PORTUGAL2020, FEDER and the Portuguese Foundation for Science and Technology (FCT) through projects PTDC/FIS-NAN/3668/2013 and POCI-01-0145-FEDER-028114. J F-R acknowledges financial support from FCT UTAPEXPL/NTec/0046/2017 project, as well as Generalitat Valenciana funding Prometeo2017/139 and MINECO Spain (Grant No. MAT2016-78625-C2). D L R S thankfully acknowledges the use of HPC resources provided by the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil). A T C thankfully acknowledges the use of computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-FI-2019-2-0034

One-armed spiral instability in double-degenerate post-merger accretion disks

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record.Increasing observational and theoretical evidence points to binary white dwarf mergers as the origin of some if not most normal Type Ia supernovae (SNe Ia). In this paper, we discuss the post-merger evolution of binary white dwarf (WD) mergers, and their relevance to the double-degenerate channel of SNe Ia. We present 3D simulations of carbon-oxygen (C/O) WD binary systems undergoing unstable mass transfer, varying both the total mass and the mass ratio. We demonstrate that these systems generally give rise to a one-armed gravitational spiral instability. The spiral density modes transport mass and angular momentum in the disk even in the absence of a magnetic field, and are most pronounced for secondary-to-primary mass ratios larger than 0.6. We further analyze carbon burning in these systems to assess the possibility of detonation. Unlike the case of a 1.1 + 1.0M C/O WD binary, we find that WD binary systems with lower mass and smaller mass ratios do not detonate as SNe Ia up to ∼ 8−22 outer dynamical times. Two additional models do however undergo net heating, and their secular increase in temperature could possibly result in a detonation on timescales longer than those considered hereWe thank James Guillochon, Daan Van Rossum, Chris Byrohl, and Pranav Dave for useful discussions. We also would like to thank the anonymous reviewer for their useful comments and insights. The work of EG-B, GA-S and PL-A was partially funded by MINECO AYA2014-59084-P grant and by the AGAUR. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. This work used the Extreme Science and Engineering discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. Simulations at UMass Dartmouth were performed on a computer cluster supported by NSF grant CNS-0959382 and AFOSR DURIP grant FA9550-10-1-0354. RTF thanks the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the Kavli Institute for Theoretical Physics, supported in part by the national Science Foundation under grant NSF PHY11-25915, for visiting support during which this work was completed. This research has made use of resources from NASA’s Astrophysics Data System and the yt astrophysics analysis software suite (Turk et al. 2011)

On choice rules in dependent type theory

In a dependent type theory satisfying the propositions as types correspondence together with the proofs-as-programs paradigm, the validity of the unique choice rule or even more of the choice rule says that the extraction of a computable witness from an existential statement under hypothesis can be performed within the same theory. Here we show that the unique choice rule, and hence the choice rule, are not valid both in Coquand\u2019s Calculus of Constructions with indexed sum types, list types and binary disjoint sums and in its predicative version implemented in the intensional level of the Minimalist Founda- tion. This means that in these theories the extraction of computational witnesses from existential statements must be performed in a more ex- pressive proofs-as-programs theory

On Induction, Coinduction and Equality in Martin-L\uf6f and Homotopy Type Theory

Martin L\uf6f Type Theory, having put computation at the center of logicalreasoning, has been shown to be an effective foundation for proof assistants,with applications both in computer science and constructive mathematics. Oneambition though is for MLTT to also double as a practical general purposeprogramming language. Datatypes in type theory come with an induction orcoinduction principle which gives a precise and concise specification of theirinterface. However, such principles can interfere with how we would like toexpress our programs. In this thesis, we investigate more flexible alternativesto direct uses of the (co)induction principles.As a first contribution, we consider the n-truncation of a type in Homo-topy Type Theory. We derive in HoTT an eliminator into (n+1)-truncatedtypes instead of n-truncated ones, assuming extra conditions on the underlyingfunction.As a second contribution, we improve on type-based criteria for terminationand productivity. By augmenting the types with well-foundedness information,such criteria allow function definitions in a style closer to general recursion.We consider two criteria: guarded types, and sized types.Guarded types introduce a modality ”later” to guard the availability ofrecursive calls provided by a general fixed-point combinator. In Guarded Cu-bical Type Theory we equip the fixed-point combinator with a propositionalequality to its one-step unfolding, instead of a definitional equality that wouldbreak normalization. The notion of path from Cubical Type Theory allows usto do so without losing canonicity or decidability of conversion.Sized types, on the other hand, explicitly index datatypes with size boundson the height or depth of their elements. The sizes however can get in theway of the reasoning principles we expect. Our approach is to introduce newquantifiers for ”irrelevant” size quantification. We present a type theory withparametric quantifiers where irrelevance arises as a “free theorem”. We alsodevelop a conversion checking algorithm for a more specific theory where thenew quantifiers are restricted to sizes.Finally, our third contribution is about the operational semantics of typetheory. For the extensions above we would like to devise a practical conversionchecking algorithm suitable for integration into a proof assistant. We formal-ized the correctness of such an algorithm for a small but challenging corecalculus, proving that conversion is decidable. We expect this development toform a good basis to verify more complex theories.The ideas discussed in this thesis are already influencing the developmentof Agda, a proof assistant based on type theory

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201